(1/3×5+1/5×7+1/7×9+…..+1/19×21) x X =9/7

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1. $(\dfrac{1}{3.5}+\dfrac{1}{5.7}+…+\dfrac{1}{19.21}).x=\dfrac{9}{7}$

   $\dfrac{1}{2}.(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+…+\dfrac{1}{19}-\dfrac{1}{21}).x=\dfrac{9}{7}$

   $\dfrac{1}{2}.(\dfrac{1}{3}-\dfrac{1}{21}).x=\dfrac{9}{7}$

   $\dfrac{1}{2}.\dfrac{2}{7}.x=\dfrac{9}{7}$

   $\dfrac{1}{7}.x=\dfrac{9}{7}$

   $x=\dfrac{9}{7}:\dfrac{1}{7}=\dfrac{9}{7}.7=9$

   Vậy $x=9$

    

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2. `(1/(3×5)+1/(5×7)+1/(7×9)+…+1/(19×21))×x = 9/7`

   `1/2 ×(2/(3×5)+2/(5×7)+2/(7×9)+…+2/(19×21))×x= 9/7`

   `1/2 ×(1/(3×5)+1/(5×7)+1/(7×9)+…+1/(19×21))×x= 9/7`

   `1/2 ×(1/3 -1/5 +1/5 -1/7 +1/7 -1/9 +1/9 -… -1/19 + 1/19 -1/21)×x= 9/7`

   `1/2 ×[1/3 +(1/5 -1/5)+(1/7 -1/7)+(1/9-1/9)+…+(1/19 -1/19)-1/21]×x= 9/7`

   `1/2 ×(1/3 +0+0+0+…+0 -1/21×)x= 9/7`

   `1/2 ×(1/3 -1/21)×x= 9/7`

   `1/2 ×(7/21 -1/21)×x= 9/7`

   `1/2 × 6/21 ×x= 9/7`

   `1/2 × 2/7 ×x= 9/7`

   `(1×2)/(2×7) ×x= 9/7`

   `1/7 ×x= 9/7`

   `x= 9/7 : 1/7`

   `x= 9/7 × 7`

   `x=(9×7)/7`

   `x=9`

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